Having a backup is pointless unless you have tried to actually replay it. Fortunately, it is easy to do. In case you have created a plain text backup, you can simply take the SQL file and execute it:
psql your_db < your_file.sql
A plain text backup is simply a text file containing everything. You can always simply replay a text file.
In case you have decided on a custom format or directory format, you can use pg_restore to replay the backup. pg_restore allows you to do all kinds of fancy things such as replaying just a part of a database and so on. In most cases, however, you will simply replay the entire database. In my example, I will create an empty database and just replay a custom format dump:
[hs@linuxpc backup]$ createdb new_db
[hs@linuxpc backup]$ pg_restore -d new_db -j 4 /tmp/dump.fc
Note, that pg_restore will add data to an existing database. In case your database is not empty, pg_restore...